Prevent Apple Watch from turning off the screen

I think that is not possible. The only big problem with turning off the screen is when you need Siri in your app. Siri waits too long before the text appears on the screen. The iPhone filters much better the background noise. But on the watch it thinks that you are not finished yet with your spoken text and waits before it analyzes the text. And then the screen turns off before you can check it.

There is currently no API to keep the watch screen on (in watchOS 1 or 2).